THE MEASURED PERFORMANCE OF A PLANEWAVE GENERATOR PROTOTYPE Clifton C. Courtney and Donald E. Voss. Voss Scientific, 418 Washington St., SE Albuquerque, NM 87108 Randy Haupt Utah State University, 4120 Old Main Hill Logan, UT 84322-4120 Larry LeDuc 412 TW / EWD, 30 Hoglan Ave. Edwards Air Force Base, CA 93524-8210 ABSTRACT The fundamental concepts of operation of a Planewave Generator1 (PWG) were described in an earlier paper. In the present paper the measured performance of a proof of performance experiment are reported. First, we will briefly describe the concepts and architecture of the experimental configuration. Next, measurements of the electromagnetic field created by the PWG prototype in a specified test zone will be presented. A planewave figure of merit (FOM) has been defined earlier, and the measured FOM of the PWG will be compared with the FOMs of the field of a single antenna, and of a uniformly illuminated transmit array. We first discuss the experimental strategy, and our use of superposition to minimize the hardware required for the demonstration. We then present measured data that shows that a minimally configured PWG can produce field distributions that are planewave-like over a limited spatial extent, and that its field demonstrates planewave qualities that significantly exceed those achievable by a typical transmit antenna, or uniformly-illuminated array. We also present data that relates the size and quality of the planewave-like field in a test zone in terms of the number of elements in the PWG transmitting array. Finally, we present a scaling relation for the PWG, and show that the radiated field produced by the experimental hardware agrees well with the field predicted by simulation. Keywords: planewave generator, far field, near field, antenna, experimental measurement, T-factor 1. INTRODUCTION The Voss Scientific Planewave Generator (PWG) concept relies on a number of transmitters operating in unison to create a desired, planewave-like field distribution over a specified and spatially limited region of space. The phase 1 Patent Pending and amplitude of the microwave signals (nominally 3 GHz for these experiments) that drive each transmit antenna of the PWG are independently controlled by a computer and microwave control circuits as described in . The purpose of the Proof of Principle (PoP) experiment described in this paper was to demonstrate the PWG concept and its potential capability, and to develop scaling laws that determine the PWG size (number of transmit channels) and configuration (physical layout) required to realize a user-specified performance criterion. To conduct the PoP with a minimal hardware investment we have designed an experiment to demonstrate PWG operation by utilizing the superposition principle of electromagnetics. Below, we describe the basic concepts of the experiment, the experimental hardware design, and data collection and reduction schemes. We then present measured data of the performance of the PWG, and compare experimental results with simulations of the PWG. Finally, we include analysis that indicates the scaling properties of the PWG. To begin, we present the experimental objectives. 2. EXPERIMENTAL OBJECTIVES The three objectives for the PoP experiment and PWG demonstration were to: • show that a minimally configured PWG system (small number of radiators) can produce useful field distributions. This means that the field distributions are planewave-like over limited (but useful) spatial extents, and demonstrate planewave qualities that significantly exceed those achievable by a standard antenna, or a uniformly-illuminated array. • show that the size and quality of the planewave-like field in a test zone is scalable with the size and number of transmitting elements in the PWG transmitting array; and • show that the radiated field produced by the PoP experimental hardware matches the field predicted by analysis and simulation(s). 3. EXPERIMENTAL CONFIGURATION 3.1 Experiment Concept – The PWG normally utilizes a number of transmitters, each with independent amplitude and phase control, to create a desired field distribution over a user-specified region of space. For the PoP experiment we have implemented a hardware design that is inexpensive (to the extent any microwave hardware is inexpensive) and easy to assemble and operate. The concept for the experiment is shown in Figure 1. In the figure a single transmit antenna and single electromagnetic field sensor are indicated. The transmit antenna is located at one possible position, and the weighted sum of the fields produced by the transmit antenna operating at each transmit position in the linear array constitutes the field of the virtual PWG indicated in the figure. The virtual PWG operates as follows. A transmit antenna is first driven by a microwave generator at a constant power level and phase. A receive probe is positioned at some distance in front of the transmitter locations, and as the transmit antenna radiates, measurements of the probe’s output signal (proportional to the electromagnetic field) are made at many positions along the extent of the distance traveled by the probe. After the first measurement is completed, the transmit antenna is repositioned to another physical site corresponding to the y location of a different transmit antenna in the PWG. Again, measurements of the radiated field are made at the same locations where the field was measured previously. This process is repeated until the field has been measured for all locations of the transmit antennas. We then utilize the principle of superposition  to synthesize the radiated field due to the simultaneous transmission of all PWG transmitters. Combining the individual field measurements with complex weighted values determined by the PWG simulations mimics PWG performance. This technique allows the demonstration of the capability of an actual PWG (one with many transmitters, and a capacity to drive each with independent and coherent signals) without the necessity of multiple transmitters. We recognize that certain aspects of the actual configuration are not created in this test, most notably transmitter mutual coupling. 3.2 PWG Test Bed Hardware Description - A custommade test bed hosts the TX and RX antennas, and a computer-controlled linear positioner. Its rigid construction of extruded aluminum unistrut permits precise and repeatable physical configuration of the PWG. The test bed, depicted in the illustration of Figure 2, was designed to allow adjustments in its physical configuration such as separation between the transmit position and receive position, heights of the transmit and receive antennas, and separation between the transmit S en so r trav els th ro ug h p la ne w av e reg ion L in ear Track P o sitio ne r T o tal field is th e S U P E R P O S IT IO N o f th e field fro m each tran sm it an ten n a E M S en sor : R e ceiv e D e sired P la ne w a ve R e gio n z = z0 R ad iated field o f tran sm it an ten n a w h en tran sm it an ten n a is at th is lo catio n R ad iated fie ld of tran sm it a nten na z = 0 Tran sm it A n te nn a (A 0 , M0 ) M icro w ave S o u rce (A 0 , M0 ) Tra ns m it statio n sep aratio n (A 0 , M0 ) (A 0 , M0 ) (A 0 , M0 ) V IR TU A L P L A N E W A V E G E N E R A T O R Figure 1 - Schematic diagram of the Proof of Principle hardware simulation of the Plane Wave Generator Once the measurements of the radiated field had been made for multiple positions of the transmit antenna, the field from an actual PWG was determined using superposition. The test zone field was synthesized from the field measurements made on the PWG test bed in two ways. The synthesized fields were formed as follows. antenna locations. Dielectric Antenna Post Receive antenna Motorized Linear Positioner Transmit antenna Al unistrut Testbed Support Frame Figure 2. PWG Test Bed. As indicated in the figure the transmit antenna is located on one side of the test bed, and manually positioned to the desired location. Fiducial markings on the base of the transmit antenna support frame assure accurate and repeatable positioning of the transmit antenna. Both Tx and Rx antennas are mounted on custom support stands made of low dielectric, non-conductive plastic material. Typically, the transmit antenna was WR-284 (2.6 – 3.95 GHz) open ended waveguide, while the receive antenna was a dual ridged waveguide horn (2 – 18 GHz). When an experiment is underway, a computer-controlled linear positioner takes the RX probe through the test zone in a precise and repeatable manner. It also issues triggers to a vector network analyzer (VNA) to record field measurements. The VNA is used to measure a standard transfer function (s21) between the transmit and receive antennas, and provide the RF signal to the transmit antenna. Absolute values of field strength are not required, since we are comparing differences in the magnitude and phase of the transmitted field distribution across a predefined region. Low loss cable was used for all RF connections to minimize loss and maximize system dynamic range. The PoP test bed is operated outdoors, far from other structures. Anechoic material was dispersed on the ground between Tx and Rx antennas to suppress the ground bounce. 3.3 Data Collection and Post-Processing Software Custom software automatically controlled the linear positioner and VNA, retrieved data from the VNA, and stored the data in a database. Computer control of the data collection process facilitated the required accurate and repeatable measurements of the radiated field of a single transmit antenna from multiple transmit positions needed to characterize the properties of an actual PWG. Synthesis Procedure No. 1: Reading from an input file that contained all run parameters (file names, geometrical parameters, electrical parameters) the PWG simulation used a genetic algorithm to optimize the transmit array magnitudes and phases (Tx weights). Measurements of the electric field made by the VNA and stored in a database, are then exported to an ASCII file of xy-pairs (position, vector field value). The post-processing software next reads in the field measurements, applies the simulationspecified amplitude and phase weighting for each channel of the transmit array, and properly combines the field measurements (add the weighted values from all files together at like positions). Again, in this case the transmit array weights (amplitude and phase) are determined a priori by a PWG simulation, and the resulting planewave field is formed from the sum of weighted measurements. Synthesis Procedure No. 2: Measurements of the electric field are made by the VNA and stored in a database; the field data is then exported to an ASCII file of xy-pairs. The second field synthesis program reads run parameters from an input file, reads in the values of the field measurements, and executes the PWG simulation software to optimize the amplitude and phase weighting needed to generate the best fit to the desired planewave. Once the weights are determined a posteriori, it forms the synthesized field in the same manner described earlier. 4. EXPERIMENTAL RESULTS This section gives an overview of the results of the experiment. These results include the measured fields of a single radiator, of a uniformly excited transmit array, and of the transmit array weighted to optimize the planewave properties over the specified region. In addition, results are presented that illustrate how the PWG can be used to simulate planewaves arriving from directions other than normal to the test zone (angle of arrival, or AoA simulation). Next, data is presented that illustrates the bandwidth characteristics of the PWG. Several comparisons of the measured PWG characteristics with simulations are then presented, and finally data is shown that indicates scaling properties of the PWG architecture. 4.1 Nominal PWG Hardware Configuration – The initial hardware configuration for the experiment consisted of: 11 transmit locations, each using open-ended waveguide as a transmit antenna, operation at a frequency = 3 GHz, a separation between transmit locations = 0.9 0.8 0.7 -1.0 Desired Planewave Region -0.5 0.0 z - meters 0.5 1.0 1.0 100 0.8 0 -100 0.6 0.4 0.2 -200 Desired Planewave Region -300 -1.0 -0.5 0.0 z - meters Desired Planewave Region 0.0 0.5 1.0 -1.0 -0.5 0.0 z - meters 0.5 1.0 Figure 3. Field of a single PWG radiator: (a) magnitude; (b) phase; and (c) T-factor. 4.3 Field of a Uniformly Excited Array – The transmit antenna was subsequently positioned at the other eleven positions that together constitute the virtual PWG. The radiated field was measured for each transmit antenna location, and the fields were combine with equal weighting factors for uniform array excitation. The resulting amplitude and phase of the field created by the PWG for uniform weighting is shown in Figure 4. The Tfactor was found to be greater than 0.59 over the region defined as the desired planewave zone. 4.4 PWG Performance – Next, the eleven field measurements were combined using weighting factors determined by the PWG optimization technique described in . The angle of arrival was specified as 0°. Shown in Figure 5 are the measured / synthesized values of the field amplitude (a) and phase (b) over the scanned area that included the desired planewave region. The T-factor over the desired planewave region was found to be greater than 0.916. These results demonstrate that the PWG can produce a field that has significantly better planewave-like properties than either a single transmit element, or a field magnitude 1.2 0.8 T > 0.59 0.4 Planewave Region 0.0 -1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 0.4 0.6 0.8 1.0 phase - degrees z - meters 40 20 0 T > 0.59 -20 Planewave Region -1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 z - meters Figure 4. Field of PWG for uniform excitation. field amplitude 1.0 T-factor Phase - degrees field magnitude 4.2 Field of One Radiator – The field of a single radiator was measured across a region that included the desired planewave zone. Shown in Figure 3 is the measured field of the middle element of the PWG array. Though the magnitude (a) of the radiated field is somewhat acceptable over the desired planewave region due to the broad beamwidth of the transmit antenna, the phase (b) is seen to deviate significantly from a planewave condition. The T-factor , shown in (c), varies between 0 and 1. This also indicates a poor planewave character for the field of the antenna. The specified / desired planewave region is indicated by the shading in the graphs. uniformly excited transmit array of the same size and configuration as the PWG. Perfect Amplitude 1.2 1.0 0.8 Defined Planewave Region 0.6 Measured Amplitude 0.4 0.2 -10 -8 -6 -4 -2 0 T > 0.916 2 4 6 8 10 z/l field phase 0.1016 m (= 1.016 λ = 4.0 inches), a separation between transmit array and planewave region = 2.5 meters, and a specified planewave region size = 1 meter in width (10 λ). The receive antenna (in the planewave region) was a dualridged waveguide horn (AEL-1498). The field was sampled at 201 points (scanned +/- 30 inches from center position), or every 0.3 inches. For reference the farfield of a single transmit radiator = 0.131 meters, while the farfield of the entire transmit array = 20.64 meters. Therefore, the planewave region is in the farfield of a single radiator, but the near field of the entire PWG transmit array. Perfect Phase 50 0 -50 Defined Planewave Region -100 Measured Phase -150 -10 -8 -6 -4 -2 0 T > 0.916 2 4 6 8 10 z/l Figure 5. Field of the PWG for optimized excitation. 4.5 Angle of Arrival Simulation – One of the more interesting possible capabilities of the PWG is its apparent ability to create fields that mimic the field of planewaves incident from angles other than the normal. Consider Figure 6 where the relationship between the angle of arrival (AoA) and the phase taper over a 1-D region is shown. phase - degrees 400 Angle of Arrival = 10 deg 200 Angle of Arrival = 7.5 deg 0 Angle of Arrival = 5 deg -200 Planewave Region -400 -0.75 -0.50 -0.25 0.00 0.25 0.50 0.75 z - meters Figure 7. PWG AoA simulation: AoA = 5; 7.5; and 10°°. To illustrate the difference, consider that the phase taper over a 10λ region for a planewave with an AoA = 10° is Φ= 2π 2π h sin(φ) = 10λ sin(10) = 10.91 Rad = 625o . λ λ For even moderately sized planewave regions, a relatively modest value for the angle of arrival can result in a very large phase taper over a region occupied by an aperture of interest. Using the same nominal hardware configuration described earlier, various AoA values were input to the PWG optimizer. The resulting excitation weights were then applied to the measured field values, and the PWG field was synthesized. The phase distribution over the scanned region for AoA = 5°, 7.5° and 10° are shown in Figure 7, the minimum values of T-factor for each case are T > 0.844, 0.748, and 0.632, respectively. As one would expect, the value of T-factor decreases as the value of apparent AoA increases. 4.6 PWG Bandwidth – For the PWG to have practical application in most testing scenarios it must exhibit a certain bandwidth. In other words, the PWG must provide planewave-like performance at frequencies about the center frequency (the frequency at which the optimized planewave solution has been determined). The field in the planewave region of the PWG was measured at frequencies 2.5 – 3.5 GHz for the physical configuration parameters described earlier. The optimized weights were determined for 3.0 GHz (AoA = 0°), then applied to the measured values at all frequencies, and the resulting PWG synthesized field was formed. The minimum values of T-factor were then computed over the specified planewave region, these values are shown in the graph of Figure 8. The graph shows an excellent solution at 3 GHz (T > 0.9), but one that declines quickly as the frequency moves away from the center frequency (T ~ 0.7 for 2.7 – 3.3 GHz). The second curve in the graph is the planewave fidelity of the solution reached by recomputing optimized array weights. This result exhibits a much greater bandwidth with T > 0.9 over the entire measurement range. Degradation in T-factor for cases where 3-GHz weights are applied at other frequencies might have more to do with the transmit and receive horn properties (variations in pattern and input impedance with frequency) than with PWG limitations. This remains an issue under study. 1.0 Minimum T-factor Figure 6. Geometry for angle of arrival. 0.9 0.8 0.7 Meas. data w/ GA optimized weights Meas. data w/ 3 GHz weights 0.6 0.5 2.4 2.6 2.8 3.0 3.2 3.4 3.6 frequency - GHz Figure 8. Bandwidth of PWG solution. 4.7 Comparisons with PWG Simulations – Of considerable interest is the agreement among measured values of PWG performance and simulated values. Shown in Figure 9 are minimum values of the measured T-factor over the desired test zone as a function of the simulated angle of arrival (for the baseline PWG configuration). Also shown in the graph are the values determined from simulation. One can note excellent agreement among the measured and simulated values. Furthermore, the graph shows that for a desired planewave region of 1.0 m (10λ at 3.0 GHz) the PWG can generate fields that mimic angles of arrival of 7.5° with T > 0.8 (phase error < 20°). 4.8 Scaling Characteristics of PWG Architecture – All results shown to this point have been for the case of 11 transmitters, with a fixed configuration (spacing separation, etc.), and for a fixed planewave region size (10λ). For design purposes it is important to know how the performance of the PWG scales with the number of transmitters. Shown in Figure 10 are minimum values of the simulated T-factor over a 10λ-wide test zone as a function of the simulated angle of arrival, for a 25transmitter PWG configuration. The graph shows that the PWG can generate fields that mimic angles of arrival to 20.0° with T > 0.8. 1.0 T-factor 0.8 Measurements Simulations 0.6 show that reasonable PWG configurations demonstrate an ability to exceed the planewave properties of conventional radiators (standard gain horn, electrically small antennas, uniformly excited Tx arrays, etc.). 0.4 1.5 0.2 0.0 0 5 10 15 20 angle of arrival - degrees Figure 9. Angle of Arrival for PWG configuration: 11 elements. Test Zone Width (m) f = 3 GHz element11 Feb. 25, 2002 2:39:38 PM Test Zone Range = 2.5 meters 1.0 Tx separation = 4 inches 0.5 tzWidth Feb. 26, 2002 9:03:27 AM 1.0 0.0 3 T-factor 7 9 11 13 15 Number of Radiators 0.8 Figure 12. Planewave region size vs. number of PWG transmitters. 0.6 0.4 0.2 element25 Feb. 25, 2002 2:40:54 PM 0.0 0 5 10 15 20 25 30 angle of arrival - degrees Figure 10. Angle of Arrival for PWG configuration: 25 elements. Next shown in Figure 11 are the minimum values of measured T-factor over the planewave region as a function of planewave region size (number of PWG transmitters = 11). The graph shows that T > 0.8 for planewave region sizes to 15λ are possible for a PWG with 11 transmitters (AoA = 0°). Also shown in the graph are the minimum values determined by simulation. Excellent agreement is again noted among measured and simulated values. Finally, the PWG test bed was used to determine how the PWG capability scales with the size (number of transmitters) of the PWG. Shown in Figure 12 is the experimentally determined maximum test zone width with a T > 0.9 as a function of the number of transmitters in the PWG array. The data shows a planewave size scaling factor of approximately 1λ / transmitter for the equally spaced arrays considered here. 1.0 field minimum T-factor 5 Simulation Measurement 0.8 0.6 N = 11 Tx separation = 4-inches Planewave region range = 2.5-m frequency = 3 GHz 0.4 0.2 TZsizeCOMP Feb. 23, 2002 12:12:33 PM 0.0 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 planewave region size / l Figure 11. T-factor vs. size of planewave region. 5. SUMMARY The purpose of the work reported in this paper was to experimentally demonstrate the concepts and operation of a Planewave Generator. First, the experimental results We have shown that the PWG demonstrates an exceptional capability to create flat amplitude tapers over a specified and spatially limited planewave region, and an extraordinary capability to create phase tapers that mimic planewaves with arbitrary angles of arrival. Also, we have illustrated that PWG simulation fields and PWG measurements are in good / excellent agreement, and that the size of the planewave region and AoA simulation capability scales with the number of radiators in the Tx array. Both simulation and measurements show sufficient practical bandwidth. Much further work remains in the design of hardware and software, and validation of a prototype PWG. 6. REFERENCES  C. Courtney, D. Voss, R. Haupt and L. LeDuc, “The Theory and Architecture of a Planewave Generator,” AMTA 2002, Cleveland, 2002.  Electromagnetic Waves and Radiating Systems, E. C. Jordan and K. G. Balmain, 2nd edition, Prentice Hall Inc., Englewood Cliffs, NJ, 1968. 7. ACKNOWLEDGMENTS This work was supported in part by the United States Air Force under the Small Business (SBIR) Innovation Research program. The authors wish to thank the following individuals for their contributions to the development of this technology: Mr. Abraham Atachbarian (EAFB SBIR Program Manager), Ms. Joanne Eldredge (EAFB Contracting Office), Mr. Mark Timmons and Mr. Ged Bluzas (EAFB, former Project Officers), Mr. Dave Slemp (Agilent Technologies), and Dr. Bill Swartz, Mr. Frank Elwood, Mr. Mike Thomas and Mr. Philip Critelli (Voss Scientific).